On a Cheeger Type Inequality in Cayley Graphs of Finite Groups
Loading...
Date
2019
Authors
Volume
20
Issue
Journal
Series Titel
Oberwolfach Preprints (OWP)
Book Title
Publisher
Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach
Link to publishers version
Abstract
[nicht gut kopierbar]Let G be a finite group. It was remarked by Breuillard-Green-Guralnick-Tao that if the Cayley graph C(G,S) is an expander graph and is non-bipartite then the spectrum of the adjacency operator T is bounded away from −1. In this article we are interested in explicit bounds for the spectrum of these graphs. Specifically, we show that the non-trivial spectrum of the adjacency operator lies in the interval [−1+h(G)⁴/γ,1−h(G)²/2d²], where h(G) denotes the (vertex) Cheeger constant of the d regular graph C(G,S) with respect to a symmetric set S of generators and γ=2⁹d⁶(d+1)².
Description
Keywords
Collections
License
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.